Non-linear magnetization dynamics of ferromagnetic insulators at parallel pumping

The non-linear dynamic equation for weakly anisotropic ferromagnetic insulators at parallel pumping in the region of frequencies less than that of the parametric resonance is derived. This equation is used for solving some non-linear problems. The process of the non-linear relaxation of magnetization is considered. The non-linear loss in energy in ferromagnets is studied in the low-frequency region ωτ_∥ ? 1, where τ_∥ is the time relaxation of magnetization connected with the dipole-dipole interaction. In the frequency region ωτ_∥ ? 1 a new type of instability is found. If the amplitude of the variable magnetic field $\text{H(t) =}\text{H}\text{+ h}\text{cos}\text{ωτ}$ satisfies the condition $\text{h}\text{H}\text{? Z}{}_{\mathrm{<mtext>c</mtext>}}\text{≈ 2}$, then the ferromagnet is characterized by the stationary homogeneous value of magnetization. In the amplitude region $\text{h/}\text{H > Z}{}_{\mathrm{<mtext>c</mtext>}}$, this state is unstable and the magnetization starts rotating. At the threshold of instability the magnetic state changes abruptly. The loss in energy in the stability region is found.